Comparison of proper motions in declination for 387 Gaia DR2 and HIPPARCOS stars from ILS observations over many decades

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Comparison of proper motions in declination for 387 Gaia DR2 and HIPPARCOS stars from ILS observations

over many decades

G. Damljanović, F. Taris

To cite this version:

G. Damljanović, F. Taris. Comparison of proper motions in declination for 387 Gaia DR2 and HIP-

PARCOS stars from ILS observations over many decades. Astronomy and Astrophysics - A&A, EDP

Sciences, 2019, 631, pp.A145. �10.1051/0004-6361/201936541�. �hal-03131368�

https://doi.org/10.1051/0004-6361/201936541 c

ESO 2019

Astronomy

&

Astrophysics

Comparison of proper motions in declination for 387 Gaia DR2 and H ipparcos stars from ILS observations over many decades ^?

G. Damljanovi´c

¹

and F. Taris

²

1 Astronomical Observatory, Volgina 7, 11060 Belgrade, Serbia e-mail:[email protected]

2 Observatoire de Paris – SYRTE, PSL Research University, CNRS/UMR 8630, Sorbonne Universités, Université Pierre et Marie Curie, LNE, 61 avenue de l’Observatoire, 75014 Paris, France

e-mail:[email protected]

Received 21 August 2019/Accepted 26 September 2019

ABSTRACT

Context.The second solution of theGaiacatalog, which has been available since April 2018, plays an important role in the realization of the futureGaiareference frame. Since 1997, the reference frame has been materialized by the optical H

ipparcos

positions of about 120 000 stars. The H

ipparcos

has been compared with and linked to the International Celestial Reference Frame (ICRF). The ICRF is materialized by means of the radio positions of extragalactic sources using very large baseline interferometry observations. Both, the H

ipparcos

^andGaiamissions belong to the European Space Agency, and it is important to note that theGaiacatalog is going to replace the H

ipparcos

^catalog.

Aims.It has been shown that the International Latitude Service zenith telescope data pertaining to ground-based surveys that span a time baseline of about 80 yr, and which are also key when measuring proper motions, could be useful for the accurate determination ofµδfor 387 ILS stars. Therefore, in this study we aim first to reduce these stars to the H

ipparcos

reference system; second, to made our original catalog ofµδ, which we refer to as the ILS catalog, for these 387 bright stars; third, to present comparison results of the four catalogs by pairs (the ILS, H

ipparcos

or HIP, new H

ipparcos

or NHIP, andGaiaDR2); and fourth, to analyze the differences inµδbetween pairs of catalogs to characterize theµδerrors for these catalogs with a special focus on theGaiaDR2 and ILS catalogs.

Methods.At seven ILS sites around the world at latitude 39.^◦1, a set of seven telescopes was used to monitor the latitude variation via observations of the same stars for about 80 yr. Here, the inverse task was applied to improveµδvalues of the 387 H

ipparcos

^stars

using the previously mentioned observations. Due to the specific Horrebow-Talcott method of the measured star pair, it is difficult to determine µδ for each single star. However, we achieved this by developing the original method and in combination with the H

ipparcos

data. We used the previously developed least squares method and formula to determine the coefficients, which describe the systematic part of differences inµδbetween the pairs of catalogs.

Results.We calculated the coefficients with the aforementioned formula (in line with the coordinates, stellar magnitude, and color index of every star) to compare ILS, HIP, NHIP, andGaiaDR2 data ofµδagainst each other by using the set of 387 stars. The presented differences ofµδshow that the systematic errors in the four catalogs are nearly at the same level of 0.1 mas yr⁻¹. This means that the DR2 and ILSµδvalues are in good agreement with each other, and with values from the H

ipparcos

^{and new H}

ipparcos

^catalogs.

Also, the random errors of differences are small ones; they are near 1 mas yr⁻¹for ILS-HIP and ILS-NHIP, and about 2 mas yr⁻¹for ILS-DR2, HIP-DR2, and NHIP-DR2. It is important to note that there is a similar level of proper motion formal errors in H

ipparcos

and new H

ipparcos

^catalogs.

Key words. astrometry – catalogs – proper motions

1. Introduction

Gaia is a mission of the European Space Agency (ESA). It started its five-year nominal operation phase in July 2014, nearly six months after launching theGaiasatellite in December 2013 (Gaia Collaboration 2016a). The goal was to collect astronom- ical data (positions, proper motions, and parallaxes) for more than one billion sources brighter than 20.7 mag inG-band, and for about 500 000 quasars (Prusti 2012). There have been two releases so far,GaiaDR1 in September 2016 and DR2 in April 2018 (Gaia Collaboration 2016b; Lindegren et al. 2018). The GaiaDR1 results are based on observations collected during the

? Full Table 5 is only available at the CDS via anonymous ftp tocdsarc.u-strasbg.fr(130.79.128.5) or viahttp://cdsarc.

u-strasbg.fr/viz-bin/cat/J/A+A/631/A145

first 14 months starting with July 2014, and DR2 result are from the first 22 months.

Here, we used the H

ipparcos

catalog data (ESA 1997) and the new H

ipparcos

catalog data (van Leeuwen 2007) to compare theµ_δvalues against those fromGaiaDR2 and ILS. The ILS is our original catalog ofµδfor 387 ILS stars (Damljanovi´c & Pejovi´c 2006). The epoch of the H

ipparcos

catalog is J1991.25, and it was the first satellite catalog with about 120 000 stars. It was an ESA mission as well, and that catalog appeared in 1997 as a new reference frame (the ICRS in the optical domain).

To obtain the original ILS catalog ofµδvalues for 387 stars and to improve theµ_δHfrom the H

ipparcos

catalog, we took into account the latitude variations made using instruments at seven sites (see Table 1) during the period of 1899.7–1979.0.

We note that approximately an 80-year-long period of ILS data is necessary to get accurateµ_δvalues. The ILS data were included

A&A 631, A145 (2019)

Table 1.ILS stations, their geographic coordinates (longitudeλW and mean latitudeϕ), and observed intervals.

ILS station Observed

λ_W(^◦) ,ϕ(39^◦8⁰+⁰⁰) interval 1. Carloforte (CA) 1899.8–1979.0

351.7 , 9.157 (break: 1943.3–1946.5) 2. Cincinnati (CI) 1899.8–1916.0

84.4 , 19.437

3. Gaithersburg (GT) 1899.8–1979.0

77.2 , 13.309 (break: 1915.0–1932.6) 4. Kitab (KZ) 1930.8–1979.0

293.1 , 2.057

5. Mizusawa (MZZ) 1900.0–1979.0 218.9 , 3.687

6. Tschardjui (TS) 1899.7–1919.3 296.5 , 11.334

7. Ukiah (UK) 1899.7–1961.0 123.2 , 12.161

as input data into the Bureau International de l’Heure (BIH) in Paris as part of the Earth rotation programs to produce the Earth orientation parameters (EOP).

In the following, we present information aboutµδdata from the ILS and the other previously mentioned catalogs. In the next section, the calculation steps necessary to obtain the proper motion in declination for 387 ILS stars are performed. The error analysis, for random and systematic errors, regarding the com- parison ofµδbetween the four catalogs is found in Sect.4. The Conclusion details the main results after comparing the four catalogs by pairs, and recommendations are given about use- ful ground-based data in the framework of the satellite Gaia mission.

2. ILS, Hipparcos, andGaiaDR2 data

GaiaDR2 contains results for about 1.69 billion sources in the G magnitude range from 3 to 21 and at the reference epoch J2015.5. There are about 1.33 billion sources with five astro- metric parameters (coordinates, proper motions, and parallaxes) and the approximate positions for 0.36 billion faint objects. For 1.33 billion sources, the median uncertainty in position and par- allax is about 0.04 mas for sources withG<14 mag at J2015.5, and in the proper motion, the uncertainty is 0.05 mas yr⁻¹. The GaiaDR2 optical reference frame is aligned with the ICRS via quasars (Lindegren et al. 2018). Due to calibration issues, the stars with G < 6 mag mostly have inferior astrometry; here, about one third of ILS stars are in that group (see Fig. 2).

The DR1 solution (orTycho-Gaiaastrometric solution) incorpo- rated astrometric H

ipparcos

^andTycho-2 data (Lindegren et al.

2016), but the DR2 solution is independent of H

ipparcos

^and

Tycho-2 catalogs. In both solutions (DR1 and DR2), the sources are treated as single stars; for unresolved binaries the presented data thus refer to the photocenter. For resolved binaries, the results are sometimes spurious due to the confusion of the com- ponents.

The H

ipparcos

^{catalog is the optical} counterpart (Kovalevsky et al. 1997) of the ICRF. The H

ipparcos

^stars

(118 218 ones) are brighter than V-mag 12. Mostly, they are between 7 mag and 9 mag. The errors in position and parallax are about 1 mas at J1991.25, and in the proper motion about

1 mas yr⁻¹, but the errors of proper motion are larger in the case of double stars than for single ones. The main reason is due to the observation period, which was less than four years (Vondrák et al. 1998). The new H

ipparcos

catalog has appeared to improve the coordinates, proper motions, and parallaxes of stars. (van Leeuwen 2007) performed a new reduction of raw H

ipparcos

observations, and the new astrometric data are better by a factor of 2.2 in total weight, and by up to a factor of four for almost all stars that are brighter than 8 mag. All ILS stars here are brighter than 8 mag (see Fig.2). Finally, it is possible to get more accurate values, pertaining to positions and proper motions, by combining the ground-based and satellite data (such as H

ipparcos

data) with those from the H

ipparcos

catalog. This is the case for ARIHIP, the Earth Orientation Catalog (EOC;Vondrák et al. 2003), and also other catalogs.

There have been many astrometric ground-based observa- tions of the same stars, which are found in ILS data, referred to the H

ipparcos

catalog, and made using many instruments dur- ing the last century. In the case of ILS data, 387 H

ipparcos

stars were observed at seven stations (Carloforte, Cincinnati, Gaithersburg, Kitab, Mizusawa, Tschardjui, and Ukiah), cover- ing the period from 1899.7–1979.0 (see Table1). Our ILS cat- alog of µ_δ (Damljanovi´c & Pejovi´c 2006) yields accurate data for 387 stars that are common to ILS and H

ipparcos

^{. To get}

precise µ_δ via ILS data, we took a reverse approach by using latitude observations and combined these ground-based data with satellite H

ipparcos

data. The original method was applied (Damljanovi´c 2007); the corrections∆µ_δof suitable H

ipparcos

µδ_Hwere calculated and applied to the correspondingµδ_Hvalues.

Finally, the ILS values µ_δ for 387 stars show a high accuracy and are in good agreement withGaiaDR2, H

ipparcos

^{, and new}

H

ipparcos

^values.

3. Calculation of proper motion in declination of 387 ILS stars using latitude observations

3.1. ILS latitude observations

The error ofµ_δis in line with 1/∆t. Because of it, using a long ILS time interval of about 80 yr makes it possible to get a better accuracy ofµ_δ(for 387 ILS stars) than for the H

ipparcos

^stars.

Even the accuracy of H

ipparcos

star positions are better than those from ground-based surveys. Also, there are many obser- vations of the same ILS star pair (from a few to a few hundred times) per each year for the period from 1899.7 to 1979.0. Even about 0⁰⁰.2 of zenith-telescope accuracy, the long time interval (from a few decades to potentially about 80 yr), and numerous observations per year are of importance for better accuracy of ILS µδ values than for the H

ipparcos

values. Plus, by com- bining the ILS observations with suitable H

ipparcos

^{data for}

the common stars, we can get better results than if only ground- based data are used. The point of H

ipparcos

data is done for the epoch 1991.25, and during calculation we used suitable weights for all points, which were inversely proportional to position errors (Damljanovi´c et al. 2006). The tectonic plate motion and the mean latitude were removed from the ILS observations (Von- drák, priv. comm.); more information about ILS can be found in the publication byYumi & Yokoyama(1980).

In accordance with the Horrebow-Tallcott method, the main zenith-telescope (ZT) formula to calculate latitudeϕ_Pfrom a star pair and for the moment of measurementtisϕP=(δS−δN)/2+

∆z/2. The valuesδ_Sandδ_Nare the apparent declinations of stars (south star and north star, respectively) in the star pair, and the zenith-distance difference∆z=z_S−z_Nis from ZT observations.

A145, page 2 of6

-80 -60 -40 -20 0 20 40 60 80

0 5 10 15 20

DEC[deg]

RA [h]

Fig. 1.Distribution of 387 stars on celestial sphere.

Valuesδ_Sandδ_Nwere calculated by using the H

ipparcos

^cat-

alog. If we remove the polar motion term and systematic errors (instrumental, local, etc.) from the latitude data, the residuals are catalog errors that is of interest to us (Damljanovi´c et al. 2006).

3.2. Proper motions in declination using latitude observations In line with∆ϕP+(dϕP/dt)t≈(∆δS+ ∆δN)/2+t(∆µδ_S+ ∆µδ_N)/2 (Vondrák et al. 1998), we can obtainaandbby using the least square method (LSM) and linear model resn =a+b(tn−1991.25) on input points with weights. The values∆δS and∆δNare cor- rections of declinations,∆µ_δSand∆µ_δNare corrections of proper motions in declination, t is time, resn is the star pair residual, tn (in years) is the epoch of res_n,apertains to (∆δ_S+ ∆δ_N)/2, andbpertains to (∆µδ_S+ ∆µδ_N)/2. The residuals of latitude vari- ations res_n are without polar motion and the systematic terms (Damljanovi´c 2005),a andbare in accordance with the epoch 1991.25.

There is one equationb=(∆µ_δS+∆µ_δN)/2, but two unknowns

∆µδ_S and∆µδ_N. To solve that problem, we introduced one more Eq. (1), as part of our original procedure,

∆µδ_S−∆µδ_N =(µδ_S1−µδ_S2)−(µδ_N1−µδ_N2), (1) whereµ_δS1andµ_δN1are from the EOC-2 catalog (Vondrák 2004), andµδS2 andµδN2 are from the H

ipparcos

catalog. About the errors,∆µ_δS and∆µ_δN are standard deviation of∆µδ_Sand∆µδ_N, respectively. There is one equation (²∆µδS +²∆µδN)/2=_b²but two unknowns∆µδS and∆µδN. To solve that problem, we per- formed one more Eq. (2):

∆µ_δS/∆µ_δN =∆µ_δS1/∆µ_δN1, (2) where∆µ_δS1 and∆µ_δN1 are from EOC-2;∆µ_δS1 and∆µ_δN1 are the errors of stars S (south star) andN (north star) of the ILS star pair, respectively. In that direction, it is possible to calculate corrections∆µ_δSand∆µ_δN(with their errors) of each star pair for common ILS and H

ipparcos

stars, to apply these corrections to corresponding H

ipparcos

^valuesµδH, and to obtain the ILS cat- alog with proper motions in declination for each star separately.

After which, it is of interest to compare theseµδvalues of 387 stars withGaiaDR2, H

ipparcos

, and new H

ipparcos

^values.

This is especially the case forGaiaDR2 because the ILS catalog depends of H

ipparcos

and EOC-2 data.

0 50 100 150 200 250

2 3 4 5 6 7 8 9 10

Number

V [mag]

Fig. 2.Distribution of magnitudes of 387 stars.

4. Results

In Fig.1, the distribution of 387 stars on the celestial sphere is presented. The values of 0^h < α < 24^h, but 20^◦ < δ < 60^◦; it is possible to investigate the systematics (via the comparison of four catalogs of pairs by using suitable differences ofµ_δ) over all α(see Fig.3), but over just a part ofδ(see Fig.4). The distribu- tion ofVmagnitude is presented in Fig.2(4 <V <8, mostly ILS stars are from 6 to 7 mag), and the differences as function of V magnitude are presented in Fig.5. Suitable mean proper motion differences (as a function ofα,δ, andVmagnitude) are presented in Figs.3–5.

The average values of µδ (mas yr⁻¹) of 387 stars for the ILS catalog, which are also in line with V magnitude, are in Table 2. That value in the case of all H

ipparcos

^{stars is}

about ±1 mas yr⁻¹, and it is slightly better in the case of new H

ipparcos

^.

Figures 3–5 indicate some systematic errors between the mean data values from the catalog pairs. Differences between ILS and DR2 are somewhat higher in the central part of Fig.3 (at 12^hofα), and there is a small sinusoidal curve with an ampli- tude ofA=0.7±0.5 mas yr⁻¹calculated using LSM. Differences presented in Fig.4are mostly near zero; also,δis just in an inter- val from 20^◦to 60^◦. In Fig.5, only for stars fainter than 7 mag in theVband are the differences slightly higher than for the other stars. This means that the ILS values ofµ_δare in good agreement with DR2, H

ipparcos

, and new H

ipparcos

data. In Figs.3–5, the mean error bars are from±0.01 mas yr⁻¹to±0.07 mas yr⁻¹ for the plotted mean differences.

The µδ differences (or ∆) on α, δ, and V magnitude (in Figs.3–5) are small, but we tried to calculate random and sys- tematic errors of pairwise differences of 387 common stars from the catalogs using the following formula (Ivanov & Yatsenko 2003):

k₁+k₂(V−V₀)+k₃(B−V)= ∆, (3) where V0 = 6.28 is the mean value of V magnitudes and (B − V) is the color index of a star. The unknowns k1, k2, and k3 are determined using LSM and presented in Table 3;

they describe the systematic part of µδ differences. Also, in Table 3 the sum s0 of the random errors for both catalogs is found. Meaning, s0 is the random part of ∆ (the unit weight error of the solution of the system). It is calculated as s₀ = n ₁

387−3

P387

n=1[∆n−(k1+k2(Vn−V0)+k3(B−V)n)]²o1/2

where 1≤ n≤387.

A&A 631, A145 (2019)

-1.0 -0.5 0.0 0.5 1.0

0 5 10 15 20

Differences[mas/yr]

RA [h]

Fig. 3. Mean proper motion differences as function of α: ILS-HIP (cross), ILS-NHIP (open rectangle), ILS-DR2 (open circle).

-1.0 -0.5 0.0 0.5 1.0

10 20 30 40 50 60 70

Differences[mas/yr]

DEC [deg]

Fig. 4.Mean proper motion differences as function ofδ; designations are the same as in Fig.3.

In the ILS and HIP as well as the ILS and NHIP cases, the values0 ≈1 mas yr⁻¹. However, in the case of ILS and DR2, it is close to 2 mas yr⁻¹. The value 1 mas yr⁻¹is the level of errors of all H

ipparcos

^µδdata. As previously mentioned,GaiaDR2 stars withG<6 mag have inferior astrometry (Lindegren et al.

2016), and this could be the reason fors₀ ≈2 mas yr⁻¹in com- bination for ILS and DR2. The coefficients k1, k2, and k3 (in Table 3) are small for any combination of catalogs, and their standard errors are higher than the corresponding values. As we can see, the random and systematic errors of∆ are small and mostly close to each other. The valuesµ_δ of four catalogs are with high accuracy and no significant relationship between ∆ and (V−V₀) (also, (B−V)) exists in any pair of catalogs. Using 387 stars here, the valuesµδ ofGaiaDR2, which are indepen- dent and based on 22 months ofGaiaobservations, are in good accordance with ILS data.

There are 18 double and multiple stars in the ILS catalog (see Table 4); some information is from H

ipparcos

^{and the}

Sixth Catalog of Orbits of Visual Binary Stars. In three cases, the orbital periodP <100 yr, and the orbital motion of double and multiple stars, can influence proper motions. This depends onP. The short period of H

ipparcos

observations is negligible

-1.0 -0.5 0.0 0.5 1.0

3 4 5 6 7 8

Differences[mas/yr]

V [mag]

Fig. 5. Mean proper motion differences as function of magnitude;

designations are the same as in Fig.3.

Table 2.Average value ofµδof catalog ILS using 387 stars.

Average value ofµδ

[mas yr⁻¹] ILS, 387 stars ±0.21 Vmag from 4 to 5 ±0.17 Vmag from 5 to 6 ±0.21 Vmag from 6 to 7 ±0.21 Vmag from 7 to 8 ±0.18

Table 3.Comparison of 387µδ values from catalogs ILS, HIP, NHIP, andGaiaDR2 to calculate formal and systematic errors.

Catalog ,s0[mas yr⁻¹] k1,k2,k3

[mas yr⁻¹]

ILS-HIP , 1.11 −0.03 ,+0.04 ,+0.04

±0.09±0.09±0.10 ILS-NHIP , 1.16 −0.05 ,−0.02 ,+0.04

±0.10±0.09±0.11 ILS-DR2 , 2.01 −0.05 ,+0.10 ,+0.14

±0.17±0.16±0.18

in comparison with most of the P values. It is not the case of ILS data because the observational period is almost 80 yr.

Regarding theGaiaDR2, the published data refer to the photo- center for unresolved binaries. The ILS, H

ipparcos

^{, andGaia}

DR2 observations are related to different positions on the orbital arc of some double or multiple stars. That time difference is more than a half century between the middle of the ILS and H

ipparcos

epochs; there is more than three quarters of a century between ILS andGaia DR2 epochs. Here, it is of importance thatµδvalues of ILS are obtained from many decades of obser- vations. Nevertheless, some H

ipparcos

^{andGaiaDR2 proper}

motions data are not reliable even with small formal errors. This is due to many unresolved binaries, the ILS and other similar data with long histories could be useful to check even satel- lite data, such as H

ipparcos

^andGaiadata. Here, we detected two cases, H 55060 and H 117622, with bigµ_δ (mas yr⁻¹) dif- ferences between ILS and DR2, which are as follows: 16.32 for H 55060, and 14.02 for H 117622, respectively. Subsequently in A145, page 4 of6

Table 4.Detected 18 double and multiple stars (in ILS catalog) with their H

ipparcos

/WDS number, comment, and periodP(day or yr).

HIP/WDS P

10535/02157+2503 8622.7 days 15627/03212+2109 eclipsing

15737/03228+2045 no orbit 20586/04245+5051 linear

22279/04478+5318 309.9 yr 44064/08585+3548 46.8 yr 54842/11137+4105 no orbit

56274/11322+3615 81.5 yr 56613/11365+2502 no orbit

66086/13328+2421 no orbit 73068/14560+3218 no orbit 84606/17177+3717 no orbit 100643/20244+2417 no orbit 101214/20310+3656 no orbit 108372/21573+6118 no orbit 108845/22029+4439 no orbit

112871/22514+2623 383 yr 117340/23476+4650 no orbit

these cases, data of ILS, HIP, and NHIP are consistent between each other, but not with DR2. We did not find any explanation for this.

To add more information to the ILS catalog, we did a direct comparison between the NHIP andGaiaDR2 positions in dec- lination (using an epoch difference of 24.25 yr) with the ILSµδ. It is µ_δDR2/NHIP = (δ_DR2−δ_NHIP)/24.25 of a star. Two decli- nations are δDR2 andδNHIP of this star for the epochs tDR2 = 2015.5 and t_NHIP = 1991.25, respectively. The error is _µδ = (_DR2² +_NHIP² )^1/2/24.25 (Eichhorn 1974);DR2andNHIPare the standard errors ofδDR2andδNHIP, respectively. The differences (µ_δILS−µ_δDR2/NHIP), points, and main values over 3^h subinter- vals ofα, are presented in Fig.7. This is a different comparison as opposed to the one presented in Fig.3, as it compares to the positional reference frames. There are three possible sources for the observed differences: a distortion in the H

ipparcos

^posi-

tional reference frame, a distortion in theGaiaDR2 positional reference frame, or a distortion in theGaiaDR2 proper motions.

Also, any combination of these is possible. Due to a small number of stars and limited accuracy, the ILS cannot provide a definitive answer about this. We detected one case involving substantial differences betweenµδILS andµδDR2/NHIP values for star H 62145 that is 13.266 mas yr⁻¹. This is probably caused by big DR2 position error, which is±0.723 mas yr⁻¹forδ.

In Fig.6, we show the distribution of formal uncertainties on the ILSµδ. Mostly, the formal errors are until±0.25 mas yr⁻¹. This is in line with NHIP and a suitable HIP value.

5. Conclusion

We have presented the original ILS catalog of µδ data of 387 stars, and comparison results of the four catalogs by pairs (Gaia DR2, H

ipparcos

^{, new H}

ipparcos

, and ILS) via µδ of these stars. The ground-based observations of about an 80-year-long interval (during the period from 1899.7–1979.0) were done with a network of seven ILS instruments. These observations pro- vide new information about µ_δ of mentioned common ILS and H

ipparcos

stars. To obtainµδof 387 stars, the original method was applied and a combination of ILS, H

ipparcos

, and EOC-2

0 50 100 150 200 250 300 350

0.00 0.20 0.40 0.60 0.80 1.00 1.20

Number

ILS st.error [mas/yr]

Fig. 6.Distribution of standard errors inµδof ILS catalog.

-1.0 -0.5 0.0 0.5 1.0

0 5 10 15 20

Differences[mas/yr]

RA [h]

Fig. 7.Proper motion differences as function ofα, ILS-NHIP/DR2, points (cross), and mean values (circle).

data was used. The ILS catalog ofµδsatisfies the requirements of modern astrometry, and its advantage is the large number of observations together with long observation periods (several tens per star pair per year during several decades). The H

ipparcos

period of observations is less than four years and 22 months in the case of Gaia DR2. The average value of µδ of ILS is between H

ipparcos

^{, or new H}

ipparcos

^{, andGaiaDR2 ones}

values; theGaia DR2 is the best catalog. After comparing the four catalogs in pairs, good consistency between these catalogs was found with no significant discrepancies. The analysis of ran- dom and systematic errors via the (Ivanov & Yatsenko 2003) formula shows no significant relationship between the differences ofµδandVmagnitudes, nor for the color index. Using LSM, a small sinusoidal curve with amplitudeA = 0.7±0.5 mas yr⁻¹ was calculated for ILS and DR2 differences as a function ofα.

We determined µ_δ ILS values for 387 stars by calculating corrections of H

ipparcos

suitable values. As the input, the ILS latitude data (points with epochs lasting about 80 yr ILS inter- val) and the H

ipparcos

^{point (δ}for the epoch 1991.25) were used with suitable weights. Thus meaning, the ILSµδsolution is directly linked to the H

ipparcos

positions and proper motions system, but the ILS is independent of the NHIP. Therefore, there is similar behavior for the H

ipparcos

^{and ILSµ}δvalues. Differ- ences between ILS and DR2 are similar to differences between NHIP and DR2.

A&A 631, A145 (2019) Table 5.ILS catalog ofµδfor 387 stars.

HIP number µ_δ st. dev. ofµ_δ [mas yr⁻¹] [mas yr⁻¹] 19 −15.03 0.39 106 −11.46 0.15

. . . .

117622 −74.80 0.57

118224 −2.75 0.08

Notes.Full table is available at the CDS.

The systematic errors ofµδ could be larger for double and multiple stars because of the influence of the orbital motion on proper motions. That effect of the orbital motion and proper motions are difficult to separate from each other; especially using short periods of satellite missions, such as H

ipparcos

^andGaia.

However, ground-based data, such as ILS data, are of impor- tance. Here, part of the random and systematic errors could be in line with orbital motions of double and multiple stars, and astrometric binaries could be a reason for some discrepancies, which are still unrecognized, between the data from the catalogs.

It is necessary to continue investigating astrometric binaries. In the ILS catalog, we found 18 double and multiple stars (using H

ipparcos

and WDS data), but there could be more of them.

With the ILS data, we checked over the other three catalogs, and these catalogs are consistent between each other. We hope that these investigations provide more information about the Gaia DR2 data. The presented results are in line with the activity of the IAU Working Group on Astrometry by Small Ground-Based Telescopes. The ILS catalog (see Table 5) is available at the CDS.

Acknowledgements. We thank the referee Dr. van Leeuwen for the very con- structive comments, which helped substantially improve the manuscript. This research was supported by the Ministry of Education, Science and Technolog- ical Development of the Republic of Serbia (Project No. 176011 “Dynamics and kinematics of celestial bodies and systems”). This work has made use of data from the European Space Agency (ESA) missionGaia(https://www.

cosmos.esa.int/gaia), processed by theGaiaData Processing and Anal- ysis Consortium (DPAC;https://www.cosmos.esa.int/web/gaia/dpac/

consortium).

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